Skip to content
Woodworking Math

Stair stringer calculator

Enter the total rise and the stair's width. You get how many stringers to cut and how long a board each needs, the framing-square settings and a drawing of the cut layout to print, and how much wood is left under the notches, each checked against the American Wood Council's rules for deck stairs (DCA 6).

Finished floor (or grade) to the top of the deck or floor.
The cut on the stringer, nosing to nosing. 10 in is the IRC’s least.
Enter it if the stair must fit a space: the treads share it.
Outside to outside of the outer stringers.
More: riser limit, riser count, tread thickness
7 3/4 in is the IRC’s most; a lower one adds risers.
Leave blank for the fewest that fit the riser limit.
The bottom of the stringer is cut this much shorter, so the first step matches.

Stringers to cut

3 × 2x12 × 8 ft

17 1/4 in apart on centre; each needs 3 ft 1 1/2 in of board

Risers
4 × 7 1/2 in
Treads (notches)
3 × 10 in
Square: tongue
7 1/2 in
Square: blade
10 in
Left under the notches
5 1/4 in
Board depth for a 5 in throat
11 in
  • OK: A 2x12: DCA 6’s least for a stair stringer
  • OK: 5 1/4 in left under the notches: at least DCA 6’s 5 in
  • OK: Spans 2 ft 6 in: within DCA 6’s 6 ft for a cut stringer
  • OK: 3 ft wide: at least 36 in
  • OK: Riser within the 7 3/4 in limit
  • OK: Tread meets the 10 in minimum
  • OK: One flight can climb this high (12 ft 7 in at most)

One source: American Wood Council, the American Wood Council’s prescriptive deck guide (DCA 6)

These stringer rules are the American Wood Council’s for deck stairs (DCA 6). For a stair indoors, ask your building department what it wants; and check your local building code either way.

Why: 30 in of rise is 4 risers of 7.5 in: lay out 3 treads on a 8 ft board, 3 stringers.

Cut layout

3 stringers, 2x12, 8 ft. Rise 30 in: 4 risers of 7 1/2 in, 3 treads of 10 in.

Floor at the dashed line, upper floor's header at the right-hand plumb cut. Each notch: 7 1/2 in up, 10 in across.
  1. Clamp stair gauges on the framing square at 7 1/2 in on the tongue and 10 in on the blade, and step it 3 times along the edge.
  2. Draw the plumb cut at the top, square to the last tread, where the stringer meets the header.
  3. Cut the first stringer, check it in place, then trace it onto the others.

Nosing marks along the top edge, from the first

  1. 1: 0 in
  2. 2: 12 1/2 in
  3. 3: 25 in

Riser heights from the floor

  1. 1: 7 1/2 in
  2. 2: 15 in
  3. 3: 22 1/2 in
  4. 4: 30 in

Treads on cut stringers: 2x4 or 5/4 at least (DCA 6 Table 6), fastened at every stringer.

Why these numbers?

  1. The situation

    30 in floor to floor, 10 in treads, a stair 36 in wide.

    From your input: the rise, tread and width

  2. What that means

    The IRC limits risers to 7 3/4 in and treads to at least 10 in, all within 3/8 in of each other (2024 R318.7.5, 2021 R311.7.5).

    One source: International Code Council, the model building code , sources [1, 2]

  3. So

    Framing square: 7.5 in on the tongue, 10 in on the blade. Each notch is 6 in deep, leaving 5.25 in of the 11.25 in board.

    Arithmetic: exact by definition

  4. What that means

    Deck stair stringers are 2x12 at least, keep 5 in below the notches, span at most 6 ft when cut, sit at most 18 in apart, and number three at least (DCA 6 Figures 28 and 29).

    One source: American Wood Council, the American Wood Council’s prescriptive deck guide (DCA 6) , sources [3]

  5. The number

    The stringer stops at the top tread, one riser below the floor: 3 × √(7.5² + 10²) = 37.5 in of board, so a 8 ft length. 3 stringers, 17.25 in apart on centre.

    Arithmetic: exact by definition

  6. The number

    These stringer rules are the American Wood Council’s for deck stairs (DCA 6). For a stair indoors, ask your building department what it wants; and check your local building code either way.

    From your input: where you build

How we source these numbers

How a stringer is laid out

A cut stringer is a board with a notch for every tread. The rise sets the risers: divide it by the tallest riser you will accept (7 3/4 inches under the IRC) and round up, then share the rise equally among them. There is one tread fewer than risers, because the upper floor or deck is the last step, so the stringer stops at the top tread and is cut plumb where it meets the header.

That is why the board is shorter than the stair's full diagonal: it needs the number of treads times the diagonal of one step, the square root of the riser squared plus the tread squared. Lumber comes in even lengths, so the calculator names the next one up. Cut the bottom shorter by the tread's thickness and every step comes out the same height, the board a little shorter again.

Board size, span and how many

Every notch takes wood out of the board. What is left, the throat, is the depth of the board less the notch, measured square to the edge. DCA 6 asks for 2x12 stringers with at least 5 inches left, so a steep riser on a deep tread can fail even on a 2x12. A cut stringer may span 6 feet; past that, set a 4x4 post under it on a 12 inch round or 10 inch square footing, 6 inches thick, add a landing, or use solid stringers with the treads on ledgers. Cut stringers sit no more than 18 inches apart, and a stair on cut stringers alone has at least three.

DCA 6 is written for deck stairs. Indoors, ask your building department what it wants, and check your local building code either way. The stair calculator works from the same numbers and adds the headroom opening and the comfort rules; the stair code requirements list every IRC limit; the deck calculator frames the deck the stair comes down from; and the 2x12 actual size page shows why a 2x12 is 11 1/4 inches deep.

Sources

  1. American Wood Council, DCA 6-15, Prescriptive Residential Wood Deck Construction Guide: Stair Requirements, Figures 28 (stringers), 29 (tread connections), 34 (stair footing) and Table 6, pages 20–22, read 2026-11-08
  2. International Code Council, 2024 International Residential Code, Chapter 3: R318.7 Stairways, R320 Handrails, R321 Guards (free read-only text), read 2026-11-07
  3. International Code Council, 2021 International Residential Code, Chapter 3: R311.7 Stairways, R312 Guards (free read-only text), read 2026-11-07
  4. Swanson Tool Co., The Pro Reference (Blue Book), ch. 5: stair stringer layout, read 2026-11-07
  5. Fine Homebuilding, 2 rules for comfortable stairs; How to cut stair stringers, read 2026-11-07
  6. JLC (Journal of Light Construction), Stair stringers: calculation and layout, read 2026-11-07
  7. NIST, PS 20-25 American Softwood Lumber Standard, Table 3: minimum dressed sizes, read 2026-11-07

How we source these numbers